CN111131028B

CN111131028B - Inter-domain route recovery method based on minimum spanning tree of degree constraint

Info

Publication number: CN111131028B
Application number: CN201910985081.8A
Authority: CN
Inventors: 王禹; 陈素霞; 王旭辉; 周岩; 刘珺; 李松阳; 焦飒镧
Original assignee: Henan Institute of Engineering
Current assignee: Henan Institute of Engineering
Priority date: 2019-10-16
Filing date: 2019-10-16
Publication date: 2021-09-21
Anticipated expiration: 2039-10-16
Also published as: CN111131028A

Abstract

The invention discloses an inter-domain route recovery method based on a minimum spanning tree with degree constraint, which is characterized in that an inter-domain route system subjected to BGP-LDoS attack is expressed as a spanning forest, and an inter-domain route recovery topology based on the minimum spanning tree with degree constraint is constructed under the condition of meeting the set degree constraint by utilizing algorithms such as a basic migration algorithm, a complex migration algorithm, a single-tree forest correction algorithm, a FT key node selection algorithm, a CT key node selection algorithm and the like; meanwhile, in the process of creating the minimum spanning tree with the orientation constraint, the node migration information during the topology generation can be recorded; the aggregation of the node degrees can be effectively controlled in the process of recovering the topology establishment, the generation of nodes with too high degrees is avoided, and the calculation complexity in the topology generation process is effectively reduced.

Description

Inter-domain route recovery method based on minimum spanning tree of degree constraint

The technical field is as follows:

the invention relates to the field of internet security, in particular to an inter-domain route recovery method based on a minimum spanning tree with degree constraint.

Background art:

with the rapid development of the internet, an Inter-domain routing system (Inter-domain routing system) is used as a key infrastructure of the internet, and the security protection pressure faced in recent years is gradually increased. Currently, the main threats of the inter-domain routing system mainly come from the routing Prefix hijacking (Prefix hijacking), the Route leakage (Route leak) and the Low-speed Denial of Service (BGP-LDoS). BGP-LDoS is better in terms of attack speed and intensity. BGP-LDoS attacks have been escalated in threat and complexity through the initial Shrow and FB-Shrow, to ZMW and CXPST, and to variant IHD, DNP and LAAEM.

The BGP-LDoS attack can cause the local to overall failure of the inter-domain routing system, the area range of intelligent network node deployment is continuously expanded along with the development of the Internet of things, the number of potential zombie networks available for an attacker is increased, and the BGP-LDoS attack with a large-scale zombie network as a basic attack condition can generate more profound threats to the inter-domain routing system.

The inter-domain routing system failure recovery aims to ensure communication between survival nodes after the network is attacked by using various routing recovery technologies. According to the different numbers of the nodes of the failure autonomous domain and the links between domains, the existing route failure recovery method can be divided into the route recovery based on single-chain/single-domain failure and the route recovery based on multi-chain/multi-domain failure. The Route recovery method based on single-chain/single-domain failure is represented by PS (Path distributing), BRAP (backup Route Routing protocol), Not-via and MFT2-BGP, is suitable for traditional DDoS attack or unexpected node/link failure, and is difficult to deal with a multipoint unrelated area failure scene caused by BGP-LDoS attack.

The recovery method based on multi-link/multi-domain failure is to implement dynamic switching of message forwarding paths aiming at nodes of surviving autonomous domains under the condition that a plurality of autonomous domain areas without adjacency relation are approximately and simultaneously in parallel to present a communication service interruption situation. RRL (resource Routing layers), 3R (build Route recovery), DLR (Dual Link failures recovery), CSES (Circuit Selecting by Edge software), and FCP (Failure-searching Packets) are taken as representatives. The multi-chain/multi-domain failure route recovery method has the problems of high computation complexity and storage space in the aspect of pre-computation backup subgraph generation, and more importantly, BGP-LDoS attacks take highly aggregated central nodes as attack targets, and existing RRL, MRC and other algorithms do not consider the control of node degrees in generated subgraphs, so that most backup subgraphs generated by the method in the face of BGP-LDoS attacks contain the characteristic of high-central-degree nodes, and the secondary survivability of the backup subgraphs is poor.

The invention content is as follows:

the technical problem to be solved by the invention is as follows: the method overcomes the defects of the prior art, aims at constructing the minimum spanning tree with the degree of constraint as the recovery topology, provides a basic migration algorithm, a complex migration algorithm, a single-tree forest correction algorithm, an FT key node selection algorithm and a CT key node selection algorithm, constructs a new recovery topology according to the survival topology of the attacked routing system under the condition of meeting the degree of constraint, effectively controls the problem of node aggregation while reducing the complexity of calculation of the generated recovery topology, and meets the requirement of an inter-domain routing recovery method based on the minimum spanning tree with the degree of constraint, which is superior in routing and prevents secondary attack.

The technical scheme of the invention is as follows: an inter-domain route recovery method based on a degree constraint minimum spanning tree is characterized in that: step one, establishing a mathematical model of a minimum spanning tree with degree constraint;

step two, based on Node Representation (NR), coding the inter-domain routing system subjected to BGP-LDoS attack, and representing the inter-domain routing system as Forest Representation (FoR);

step three, judging whether the FoR represents a forest only containing a single tree or not, if so, correcting the forest by using a single-tree forest correction algorithm UpdateForSingleTree () to expand the applicability of the method; if not, carrying out the fourth step;

step four, after the inter-domain routing system is attacked, a single failure autonomous domain node or a plurality of adjacent failure autonomous domain nodes are usually caused, so that judgment is carried out, and if the single failure autonomous domain node in the current inter-domain routing system fails, the fifth step is carried out; if a plurality of adjacent autonomous domain nodes fail in the current inter-domain routing system, performing a sixth step;

step five, calculating key nodes under the condition that a single autonomous domain node fails by adopting an FT key node selection algorithm KeyNodeSelectionForFT (), then implementing migration operation of the failed nodes by utilizing a basic migration algorithm FundamentTransfer (), namely FT for short, and establishing an inter-domain routing system recovery topology based on a minimum spanning tree with degree constraint;

step six, calculating key nodes under the condition that a plurality of adjacent autonomous domain nodes fail by adopting a CT key node selection algorithm KeyNodeSelectionForCT (), then implementing migration operation of the failed nodes by utilizing a complex migration algorithm ComplexTransfer (), CT for short, and establishing an inter-domain routing system recovery topology based on a minimum spanning tree with degree constraint;

further, in the step one, the Degree-constrained minimum spanning tree is a minimum spanning tree that satisfies a condition if a certain number of constraints are added to the Degree (Degree) of each vertex in the minimum spanning tree, that is, if the number of constraints is not more than a preset value. For the connectivity graph G ═ (V, E), its node set V ═ V₁,v₂,...,v_nThe number of nodes is | V |; set of edges E ═ E₁,e₂,...,e_kThe number of the edges is k; the weight value corresponding to each edge is w_ij(ii) a Let T denote the set of spanning trees for all satisfaction constraints in G. The degree-constrained minimum spanning tree DCMST mathematical model is defined as:

optimizing an objective function:

constraint 1: x is the number of_ij∈{0,1},i,j＝1,2,...n

Constraint 2:

constraint 3: 1 ≤ dgr_i≤dgr_c,i＝1,2,...,n

Constraint 4:

constraint 5:

wherein, c (x) in the optimization objective function represents the total cost of the spanning tree; carrying out degradation processing on the constraint, and assuming that the weights of the edges are the same; constraint 1 Medium vector x_ijIndicating a valid edge condition between node i and node j in the graph, i.e., x_ij1 indicates that an edge exists between the node i and the node j; covering n-1 edges in the representation spanning tree in the constraint 2; constraint 3 middle dgr_iFor the value corresponding to node i, it needs to satisfy [1, d_c](ii) a range requirement; constraint 4 is intended to prevent spanning tree loop problems; constraint 5 indicates that the sum of all node values is 2 (n-1).

Further, in the second step, Node Representation (NR) is proposed, which is intended to facilitate Node encoding in the graph, and for a simple undirected graph G ═ V, E, there is a forest of generation F ═ V, E_F) Is an acyclic subgraph of G, one tree in F being T ═ V_T,E_T) Is a linking moiety of F, having

For a graph G and one of the trees T,

is composed of a node set V_TA sub-graph of the generated, i.e.,

all contained edges (x, y) are E and all the edges satisfy x is V_TAnd y ∈ V_T。

For a tree T (Root), defining the depth of a node n is the path length from n to Root, and is denoted by dp (n). N is a radical of_G(n) represents a set of nodes adjacent to node n in G. Degree of a node in G is denoted dgr_G(x) And the degree of a node in T is represented as dgr_T(x) In that respect The degree of one T in G is recorded as dgr_G(T) is the entry of the edge set E for G belonging to V_TTotal number of edges of the rendezvous node. Similarly, the number of edges in T is dgr_T(T)＝|V_T|-1。

The NR encoding table of a tree T is an ordered list in which each node NR covers four elements (n, id, dp, dgr): respectively representing nodes (identifiable by an autonomous domain number ASN in the interdomain routing system), indexes, node depths, and node degrees. The arrangement order between the nodes NR needs to satisfy: first, the nodes of each subtree are consecutive, and second, the root of each subtree precedes its node. For a node n, according to the NR notation, id (n) indicates its index value, dp (n) and dgr_G(n) respectively represent the depth and the value of the depth. For a tree T, considering the sequential characteristic of the depth-first search for the node, when implementing NR coding based on the depth-first rule, an unvisited node is found, and the node and the corresponding depth value can be added to the NR coding sequence.

The NR code FoR a spanning tree F, denoted Forest Representation (FoR), is the NR merge FoR each tree T in F. Since a forest contains multiple trees, a dual (p) can be used_T,dgr_T) A tree is represented, the former representing a pointer to the tree T and the latter representing the value of the tree.

Further, in the third step, since the subsequent migration operation assumes that at least two trees exist in one forest, in order to expand the applicability of the algorithm, the forest with only one tree may be modified, and the operation is performed according to a special manner. Therefore, a single-tree forest correction algorithm UpdateForSingleTree () is provided.

Further, in the fifth step, the FT key node selection algorithm keynode selection f FT () is intended to calculate a new tree T in FT_dstMiddle node T, and migrated subtree T_originR in (1). The fundamental migration fundamental transfer () algorithm is mainly used for constructing a new forest aiming at a typical scene that a certain key node in an inter-domain routing system fails after BGP-LDoS attack and effectively meeting the mathematical model requirement of a minimum spanning tree with degree constraint.

Further, in the sixth step, the CT key node selection algorithm keynode selection nforct () is intended to calculate the migrated tree T_originR in (1); pruning a node f; new tree T_dstNode t in (1). The complex migration ComplexTransfer () algorithm is more complex relative to FT operation, and mainly aims at a situation that a plurality of adjacent autonomous domain nodes fail after an inter-domain routing system is attacked by BGP-Ldos, and utilizes a CT algorithm to generate a minimum spanning tree with the constraint of the generation degree to implement route recovery. The complex migration ComplexTransfer () algorithm can effectively meet the mathematical model requirement of the minimum spanning tree with degree constraint.

Further, in the fifth step and the sixth step, in the process of node migration and change, the process is recorded in a manner that a coding matrix is created and gradually perfected by using a node migration coding algorithm TransNodesEncode ().

The invention has the beneficial effects that:

1. the invention uses the design concept of centralized network control for reference, plans the survival route after the BGP-LDoS attacks the routing system between the domains, and constructs a new recovery topology according to the survival topology of the attacked routing system under the condition of satisfying degree constraint through a basic migration algorithm and a complex migration algorithm.

2. The routing recovery method based on the minimum spanning tree with degree constraint can effectively and simultaneously deal with single node failure scenes in an inter-domain routing system possibly caused by BGP-LDoS and multiple adjacent autonomous domain node failure scenes.

3. The invention can effectively control the aggregation of the nodes in the process of generating the minimum spanning tree, namely recovering the topology of the routing system, and avoids generating the nodes with over-high degree.

4. The route recovery method based on the minimum spanning tree with degree constraint, disclosed by the invention, has the advantages that the computational complexity can completely meet the requirement of rapid generation of the recovery route in a multi-domain environment, and the problem of high computational complexity in the aspect of generation of backup sub-graphs in the conventional multi-chain/multi-domain recovery method is solved.

5. The invention adopts a mode of generating a forest instead of a tree to find the most appropriate scheme, and simultaneously records the node migration information during topology generation through a node migration coding algorithm in the process of creating the minimum spanning tree, thereby being convenient for backtracking and error correction.

Description of the drawings:

fig. 1 is a flowchart of an inter-domain route recovery method based on a degree-constrained minimum spanning tree.

Fig. 2 is a diagram of DCMST generation times at different graph scales with a constraint of 3.

Fig. 3 is a diagram of DCMST generation times at different graph scales with a constraint of 4.

Fig. 4 is a graph of DCMST generation times at different graph scales with a restriction of 5.

Fig. 5 is a graph of DCMST generation time at different graph scales with a restriction of 6.

FIG. 6 is a DCMST generation time comparison diagram under the constraint of different degrees of B _ tpl samples.

FIG. 7 is a comparison graph of DCMST generation time under the constraint of different degrees of W _ tpl samples.

The specific implementation mode is as follows:

example (b): see fig. 1, 2, 3, 4, 5, 6 and 7.

An inter-domain route recovery method based on a minimum spanning tree with degree constraint is characterized in that an inter-domain route system subjected to BGP-LDoS attack is expressed as a spanning forest, and an inter-domain route recovery topology based on the minimum spanning tree with degree constraint is constructed under the condition that the minimum spanning tree with degree constraint is met by utilizing algorithms such as a basic migration algorithm, a complex migration algorithm, a single-tree forest correction algorithm, an FT key node selection algorithm, a CT key node selection algorithm and the like. The method comprises the following steps: step one, establishing a mathematical model of a minimum spanning tree with degree constraint;

and sixthly, calculating key nodes under the condition that a plurality of adjacent autonomous domain nodes fail by adopting a CT key node selection algorithm KeyNodeSelectionForCT (), then implementing migration operation of the failed nodes by utilizing a complex migration algorithm ComplexTransfer (), which is called CT for short, and establishing an inter-domain routing system recovery topology based on a minimum spanning tree with degree constraint.

The present application is described in detail below.

In the field of computer and communication network design optimization, a Degree-Constrained Minimum Spanning Tree (DCMST) has been widely used, and its related definitions include:

spanning tree refers to a connected graph G ═ V, E if a subgraph thereof is a tree containing all vertices in GThis subgraph is called the Spanning Tree of G (ST), which satisfies the connected and acyclic properties, it should be noted that the Spanning Tree of the connected graph G is not exclusive. The minimum spanning tree means that for a weighted graph G (V, E) without directional connectivity, each side (V) is a weighted graph_i,v_j) The corresponding weight is w_ijIf the weight sum of a certain Spanning Tree is Minimum, then a Minimum Spanning Tree (MST) denoted as G is similar to the connected graph, and the Minimum Spanning Tree is not unique.

The term "Degree-constrained minimum spanning tree" means that if a certain number of degrees (Degree) for each vertex in the minimum spanning tree is limited, that is, the Degree of each vertex does not exceed a preset value, the minimum spanning tree satisfying the condition is regarded as the Degree-constrained minimum spanning tree. For the connectivity graph G ═ (V, E), its node set V ═ V₁,v₂,...,v_nThe number of nodes is | V |; set of edges E ═ E₁,e₂,...,e_kThe number of the edges is k; the weight value corresponding to each edge is w_ij(ii) a Let T denote the set of spanning trees for all satisfaction constraints in G. The DCMST mathematical model may be defined as:

optimizing an objective function:

constraint 1: x is the number of_ij∈{0,1},i,j＝1,2,...n

Constraint 2:

constraint 3: 1 ≤ dgr_i≤dgr_c,i＝1,2,...,n

Constraint 4:

constraint 5:

wherein, c (x) in the optimization objective function represents the total cost of the spanning tree; aboutVector x in bundle 1_ijIndicating a valid edge condition between node i and node j in the graph, i.e., x_ij1 indicates that an edge exists between the node i and the node j; covering n-1 edges in the representation spanning tree in the constraint 2; constraint 3 middle dgr_iFor the value corresponding to node i, it needs to satisfy [1, d_c]The range requirement; constraint 4 is intended to prevent spanning tree loop problems; constraint 5 indicates that the sum of all node values is 2 (n-1). It should be noted that, considering that the typical BGP-LdoS attack at present mostly does not consider the role of the weights in the topology, the present application performs degradation processing on the above constraints, and assumes that the weights of the edges are all the same.

For the spanning tree coding, a Node Representation (NR) is proposed to facilitate the Node coding in the figure. For a simple undirected graph G ═ (V, E), there is one resulting forest F ═ (V, E)_F) Is an acyclic subgraph of G, one tree in F being T ═ V_T,E_T) Is a linking moiety of F, having

For a graph G and one of the trees T,

is composed of a node set V_TA sub-graph of the generated, i.e.,

For a tree T (Root), defining the depth of a node n is the path length from n to Root, and is denoted by dp (n). N is a radical of_G(n) represents a set of nodes adjacent to node n in G. The degree of a node in G is denoted dgr_G(x) And the degree of a node in T is represented as dgr_T(x) In that respect The degree of one T in G is recorded as dgr_G(T) is the entry of the edge set E for G belonging to V_TTotal number of edges of the rendezvous node. Similarly, the number of edges in T is dgr_T(T)＝|V_T|-1。

NR coding table of tree TIs an ordered list, where each node NR covers four elements (n, id, dp, dgr): respectively representing nodes (identifiable by an autonomous domain number ASN in the interdomain routing system), indexes, node depths, and node degrees. The arrangement order between the nodes NR needs to satisfy: first, the nodes of each subtree are consecutive, and second, the root of each subtree precedes its node. For a node n, according to the NR notation, id (n) indicates its index value, dp (n) and dgr_G(n) respectively represent the depth and the value of the depth. For a tree T, considering the sequential characteristic of the depth-first search for the node, when implementing NR coding based on the depth-first rule, an unvisited node is found, and the node and the corresponding depth value can be added to the NR coding sequence.

The NR code FoR a spanning tree F, denoted Forest Representation (FoR), is the NR combination FoR each tree T in F. Since a forest contains multiple trees, a dual (p) can be used_T,dgr_T) A tree is represented, the former representing a pointer to the tree T and the latter representing the value of the tree.

For an interdomain routing system consisting of multiple autonomous domains, it corresponds to the original graph G. When DCMST is generated in response to routing failure, the process is recorded in a mode of creating and completing coding matrix step by step as the inter-domain routing nodes are continuously migrated and changed.

Node migration encoding algorithm TransNonsEncode ()

Inputting: graph G (represent an inter-domain routing system consisting of multiple autonomous domains)

And (3) outputting: migration coding matrix M of nodes_n

The method comprises the following steps:

1. for a tree F in G_iA certain node n in (1) creates a corresponding group number Array_n＝[i,P_i,id(n)_i]I denotes the sequence number of the tree to which the node belongs, P_iTo point to the tree F_iPointer to NR code, last id (n)_iIs the index value corresponding to n in NR;

2. suppose F₁Is the first forest from G, at F₁On the basis of the above-mentioned formula (I),with the cutting and migration of nodes or subtrees, the continuously generated forest sequence is marked as L ═ F₁,F₂,…F_i]；

3. If the node n is located in a sub-tree SubTr, the slave tree F_jMigration to Tree F_kThen node n will be relocated and the migration encoding matrix of the node is recorded as

Represents Array_jTransposing;

for convenience of subsequent search, is tree F_iList of configurations [ F₁,F₂,…F_i]Record from F₁Process of changing to the last state. Also, due to the ordering of the configuration list, where the position of node n can be found to satisfy both F and_ithe predecessor exists in M_nThe matrix method.

This aspect creates new forest generations by defining a fundamentals transfer (ft) and a complextransfer (ct). Specifically, the FoR of the newly generated forest F' is generated from the forest representation FoR corresponding to the existing generated forest F. The objective of the FT and CT operations is to derive T from the forest_originSubtrees in (a set of trees) migrate to another tree T_dst。

Fundamental transfer () abbreviated as FT:

the FT is mainly used for constructing a new forest aiming at a typical scene that a certain key node in an inter-domain routing system is invalid after BGP-LDoS attack, and effectively meeting a degree constraint value.

Inputting: tree T in FoR sequence of forest F_originAnd T_dstAn index of (2); migrated subtree T_originThe root r in (1), also referred to as a pruning node at this time; new tree T_dstT, t satisfies the neighborhood of r in graph G; degree constraint value cstr

And (3) outputting: FoR of newly formed forest F

The method comprises the following steps:

1. finding T_originThe sub-tree to which the middle pruning node r belongs corresponds to the index ranges of [ id (r), id (m)]The range covers the node r and the subsequent node m thereof, and the like, and satisfies that the value dp (r) is smaller than the subsequent node. Id (m) of the successor node can be found by sequential search, considering that the id (r) value is known;

2. temporarily creating an intermediate tree T_midThe system is used for storing nodes and subtrees in the migration process;

3. will T_originMiddle index Range [ id (r), id (m)]Intra NR coded data, put into temporary T_midT is calculated by the method of (dp (n) -dp (r) + (dp (T) +1)_midId (n) of each node n;

4. creation of one sequence T'_dstComprising T_dstAnd T_midAll the nodes. A new tree is generated, and a subtree with r as a root is migrated to T'_dst. Only if dgr (t) is satisfied<When cstr +1, T is set_midInserted into T'_dstAt the (id (t) +1) index, and then dp (t) ═ dp (t) + 1; if not, skipping to the step 4, and judging the next node after the node t; if T is already T_dstIf the node is the last node, indicating that cstr is too small and finishing FT;

5. creation of sequence T'_originIncluding exclusion of T_midT other than node included_originAfter all nodes in the node, then correcting T_originMedium dgr (r) ═ dgr (r) -1;

6. the NR corresponding to forest F is copied to generate a new F'. The pointers to the old and the new trees in F 'are respectively recorded as pT'_originAnd pT'_dst；

7. Calculating dgr_G(T′_origin) And dgr_G(T′_dst) And stored in F';

8. for matrix M_nMiddle T'_originAnd T'_dstIs modified by each node n in the set.

In the FundamentTransfer algorithm, T is assumed_originThe root r index values id (r) and T_dstThe index values id (t) of (m) are unknown, and the NR backup and any portion thereof are preservedAnd keeping the order of the nodes, namely keeping the order of the nodes in the original NR.

Complex migration ComplexTransfer (), CT for short:

the CT operation is more complex than the FT operation. Aiming at a situation that a plurality of adjacent autonomous domain nodes fail after an inter-domain routing system is attacked by BGP-Ldos, a CT algorithm generation degree constraint minimum spanning tree is designed to implement route recovery. FT operation and CT operation, which complement each other, together form a differentiated application scenario faced by DR algorithm.

Inputting: tree T in FoR sequence of forest F_originAnd T_dstAn index of (2); migrated tree T_originR in (1); pruning a node f; new tree T_dstT, t satisfies the neighborhood of r in graph G; degree constraint value cstr

And (3) outputting: FoR of newly formed forest F

The method comprises the following steps:

1. finding T_originThe subtree to which the middle root node r belongs has the corresponding index ranges of [ id (r), id (m)]The range covers the node r and the subsequent node m thereof, and the like, and satisfies that the dp (r) value is less than the subsequent node;

2. temporarily creating two intermediate trees T_mid1And T_mid2The system is used for storing nodes and subtrees in the migration process;

3. will T_originMiddle index Range [ id (r), id (m)]Intra NR coded data, put into temporary T_mid1T is calculated by the method of (dp (x) -dp (r) + (dp (T) +1)_mid1Id (n) of each node n;

4.T_originnodes in the path from r to f, labeled r₁,r₂,…,r_n]Corresponding to r ═ r₁And f ═ r_n；

5. Find a path from r to f. Initialization T_mid2For empty NR, for each i (1 < i ≦ n), only if dgr (i) is satisfied<In cstr +1, copy with r_iSubtree rooted (but not including r_i-1Root subtree) to T_mid2While each of the modified addition amounts to T is modified by the method of (dp (n) -dp (r) + (dp (T)) +1_mid2Of node nA deep value; besides, dp (r) ═ dp (r) +1 and dp (f) ═ dp (f) — 1 are executed to correct the nodes r and f, respectively; if not satisfying dgr (i)<cstr +1, in step 5, for the next node r_i+1Judging; if r is_iIs already T_dstIf the last node is in the middle, indicating that cstr is too small, and ending CT;

6. to be cut subtree and T_dstConnected and combined to a new tree T'_dstI.e. containing T_dst，T_mid1And T_mid2To [ T ]_mid1T_mid2]Sequence is placed in T'_dstAt (t +1), dgr (t) ═ dgr (t) +1 is performed to correct the value of t;

7. by T_originMiddle [ T ]_tmp1T_tmp2]Out node creates T'_originWill be originally T_originSubtracting 1 from the value of the forward node in the middle f;

8. copying NR corresponding to the forest F to generate a new forest structure F ', and respectively recording pointers pointing to new and old trees in F ' as pT '_originAnd pT'_dst(ii) a Calculating dgr_G(T′_origin) And dgr_G(T′_dst) And are stored in F';

9. for matrix M_nMiddle T'_originAnd T'_dstIs modified by each node n in the set.

Single-tree forest correction algorithm UpdateForSingleTree ()

The algorithm assumes that there are at least two trees in a forest when applying both CT and FT. To extend the applicability of the algorithm, a forest with only one tree may be modified, and the operation performed in a particular manner.

Inputting: unique tree T of forest F_origin

And (3) outputting: FoR of newly formed forest F

The method comprises the following steps:

1. building a tree T_supAssistance is made, assuming that the tree contains only one node n, this node being the case

And n and T_originEach node in the network maintainsConnecting;

2. let T_dstIs T_supFT is performed, thereby T can be converted_originMiddle one tree becomes T_supSuccessor of n;

3. the original tree is changed from the root tree of n by FT or CT operation, so as to generate a new forest F'.

FT Key node selection KeyNodeSelectionForFT ()

Inputting: FoR sequence of forest F

And (3) outputting: new tree T in FT_dstMiddle node T, migrated subtree T_originRoot of Chinese Greek

The method comprises the following steps:

1. randomly searching for a T tree in F to satisfy dgr_G(T) greater than dgr_T(T), let T_originIs T. If the forest is not found, the diagram G is a single forest, and the process is stopped;

2. from T_originRandomly determining a non-root node r, dgr_G(r) is greater than dgr_T(r)；

3. From N_G(r) randomly selecting a node n if the edge (n, r) does not belong to E_TIf the value is n, the step is not carried out; then determining the index id (t) of the node t in the forest F by searching the matrix;

4. if T belongs to T_originExecuting a single-tree forest correction algorithm; otherwise, FT is performed.

CT Key node selection KeyNodeSelectionForCT ()

Inputting: FoR sequence of forest F

And (3) outputting: migrated tree T_originR in (1); pruning a node f; new tree T_dstNode t in (1)

The method comprises the following steps:

1. randomly searching for a T tree in F to satisfy dgr_G(T) greater than dgr_T(T), let T_originIs T. If the forest can not be found, the graph G is a single forest, and the process is stopped;

3. Looking for r to T_originPath of root, let i be 1 and r_iIs r, from T in the direction of the root_originStarting traversal with the step length of 1, judging each node n in the traversal process, if dp (n) is less than dp (r)_i) Then let r_i+1Is n. If i>2, then in [2, …, i-1 ]]Randomly selecting j within the range, and making f be r_j(ii) a If the whole path only comprises a node r and a root, making f be r;

4. from N_G(r) randomly selecting a node n if the edge (n, f) does not belong to E_TIf yes, making t be n, otherwise, repeating the step; then, determining the index id (t) of the node t in the forest F by searching the matrix;

5. if T belongs to T_originExecuting a single-tree forest correction algorithm; otherwise, FT is performed.

In the following description, the following embodiments are described, in which a tournament selection method is used to select a child, i.e., a spanning tree, and operand selection is 2, which corresponds to the FT migration operation and the CT migration operation, respectively. The routing failure recovery method (tree-constrained minimum spanning tree based failure recovery) based on the minimum spanning tree proposed herein is abbreviated as DR.

Example one

A BRITE topology generator is utilized to generate a random graph based on a GLP model, the random graph represents AS-level simulation topology in an interdomain routing system, and the number of nodes of the random graph is respectively set to be 10,50,100,200,400,600,800 and 1000 in a regional interdomain routing system established by taking a small-scale multi-autonomous-domain community AS a unit.

And simulating BGP-LDoS attack to implement attack on the random graph, and generating DCMST by respectively using the DR algorithm and the classical ESR algorithm provided by the application aiming at the survival nodes and the links to serve as recovery topology after the inter-domain routing system is attacked. The simulation environment is Window 10, Intel i 56200U, 16G memory. In order to be able to efficiently control the aggregation of nodes in the recovery topology, the range of values of the nodes of the generation tree is limited to [3,6 ]; the average nodularity of the random graph generated by the GLP model is 4.1. ESR, as a classical spanning tree algorithm, produces a new tree from edge set operations with specific swaps and variances. In the ESR algorithm, both the crossover probability and the mutation probability are 0.8.

Fig. 2 to 5 show a comparison of the time taken to generate DCMST by the ESR method and the DR method, respectively, for random graphs containing different node numbers, for constraint values of 3 to 6, respectively. As can be seen from the figures, in both methods, along with the relaxation of the degree value constraint, that is, the generation time is relatively shorter as the constraint value is higher, but the DCMST generation time difference corresponding to the same topology scale is smaller as a whole, for example, in fig. 2 and 5, the generation time difference is only 0.95 seconds when the degree constraint is 3 and 6 respectively based on the DR method in the random topology including 1000 nodes. In addition, the DR method proposed by the present application has a quite significant performance advantage relative to the ESR method, and the performance advantage is more prominent with the increase of the topological scale, for example, in fig. 5, when the topological scale is 600, the time gap for generating DCMST by using the DR method and the ESR method is 5.68 seconds; when the topology size is 1000, the time gap rises to 22.41 seconds. Thirdly, compared with the theoretical analysis result of the complexity of time in the previous section, the DR method has better performance under the simulation condition of the random graph.

Example two

And carrying out simulation verification by using the true Internet AS-Level topology from CAIDA, and respectively obtaining sample topologies from BGP _ tables and WHOIS. BGP _ tables and WHOIS raw data sets both contain 30,000+ nodes, and the topology covering the first 3000 AS nodes is extracted from the two raw data sets for simulation, respectively, considering that the actual inter-domain route recovery mechanism of the internet needs to be implemented within a certain range. Wherein, the local topology taken from BGP _ tables is named as B _ tpl, and the average value is 2.51; the local topology taken from WHOIS is named W tpl with an average value of 6.53.

Similar to the embodiment, the BGP-LDoS is simulated to attack the B _ tpl and W _ tpl topologies, and for surviving nodes and links, DCMST is generated by using the DR algorithm and the classical ESR algorithm proposed in the present application, respectively, as a recovery topology after the inter-domain routing system attacks. The simulation environment and ESR settings are consistent with the example, and are also limited to a spanning tree node value range of [3,6 ].

FIG. 6 shows the time comparison of DCMST generated by using DR algorithm and ESR algorithm within the range of [3-6] for B _ tpl samples. It can be seen that under the two methods, as the value constraint is relaxed, the generation time of DCMST is gradually reduced as a whole, wherein the value constraint 5 is slightly higher than the value constraint 4, but the overall trend is still reduced. Compared with an ESR algorithm, the DR algorithm provided by the application has relatively obvious advantages, and the DCMST generation time is greatly reduced.

FIG. 7 is a time comparison of DCMST generated using two algorithms within a range of degrees constraint [3-6] for W _ tpl samples. Similar to the simulation result of the B _ tpl sample, on one hand, the generation time of the DCMST is also gradually reduced along with the relaxation of the value constraint condition; on the other hand, the DR algorithm has significant performance advantages over ESR. Comparing fig. 7 with fig. 6, it can be seen that, under the same degree constraint condition, the DCMST generation time under B _ tpl sample is slightly shorter than the generation time under W _ tpl sample, and this phenomenon should occur because the average node degree in B _ tpl is smaller than the average node degree in W _ tpl, so only a relatively small number of spanning tree migration operations are required, and the overall time consumption is saved.

The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and any simple modification, equivalent change and modification made to the above embodiment according to the technical spirit of the present invention are within the scope of the technical solution of the present invention.

Claims

1. An inter-domain route recovery method based on a degree constraint minimum spanning tree is characterized in that: step one, establishing a mathematical model of a minimum spanning tree with degree constraint;

step three, judging whether the FoR represents a forest only containing a single tree or not, if so, correcting the forest by using a special implementation mode in order to expand the applicability of the method; if the forest is not a single-tree forest, directly carrying out the fourth step;

step four, after the inter-domain routing system attacks, a single failure autonomous domain node or a plurality of adjacent failure autonomous domain nodes are usually caused, so that judgment is carried out, and if the single failure autonomous domain node in the current inter-domain routing system fails, the fifth step is carried out; if the current inter-domain routing system has the defects that a plurality of adjacent autonomous domain nodes fail, performing a sixth step;

step five, calculating key nodes under the condition that a single autonomous domain node is invalid by adopting an FT key node selection algorithm KeyNodeSelectionForFT (), then implementing migration operation of the invalid nodes by utilizing a basic migration algorithm FundamentTransfer (), namely FT for short, and establishing an inter-domain routing system recovery topology based on a minimum spanning tree with degree constraint;

in the first step, the Degree-constrained minimum spanning tree is a minimum spanning tree that satisfies a condition when a certain number of degrees (Degree) of each vertex in the minimum spanning tree is added, that is, when the Degree of each vertex in the minimum spanning tree does not exceed a preset value, and a node set V ═ { V, E) of the minimum spanning tree is set as the Degree-constrained minimum spanning tree, and a connected graph G ═ V, E is set as (V, E)₁,v₂,...,v_nThe number of nodes is | V |; set of edges E ═ E₁,e₂,...,e_kThe number of the edges is k; the weight value corresponding to each edge is w_ij(ii) a T represents a spanning tree set of all satisfaction degree constraints in G; the degree-constrained minimum spanning tree DCMST mathematical model is defined as:

optimizing an objective function:

constraint 1: x is the number of_ij∈{0,1},i,j＝1,2,...n

Constraint 2:

constraint 3: 1 ≤ dgr_i≤dgr_c,i＝1,2,...,n

Constraint 4:

constraint 5:

wherein, c (x) in the optimization objective function represents the total cost of the spanning tree; carrying out degradation processing on the constraint, and assuming that the weights of the edges are the same; constraint 1 Medium vector x_ijIndicating a valid edge condition between node i and node j in the graph, i.e., x_ij1 indicates that an edge exists between the node i and the node j; covering n-1 edges in the representation spanning tree in the constraint 2; constraint 3 middle dgr_iFor the value corresponding to node i, it needs to satisfy [1, d_c]The range requirement; constraint 4 is intended to prevent spanning tree loop problems; constraint 5 indicates that the sum of all node values is 2 (n-1);

in the third step, because the subsequent migration operation considers that at least two trees exist in one forest, in order to expand the applicability of the algorithm, the forest with only one tree is corrected, and the operation is implemented according to a single-tree forest correction algorithm UpdateForSingleTree ().

2. The inter-domain route recovery method based on the degree-constrained minimum spanning tree of claim 1, wherein: in the second step, Node Representation (NR) is proposed, which is intended to facilitate Node encoding in the graph, and for a simple undirected graph G ═ V, E, there is a generated forest F ═ V, E_F) Is an acyclic subgraph of G, one tree in F being T ═ V_T,E_T) Is a linking moiety of F, having

For a graph G andin the case of one tree T, the tree T,

is composed of a node set V_TA sub-graph of the generated, i.e.,

all contained edges (x, y) are E and all the edges satisfy x is V_TAnd y ∈ V_T；

For a tree T (Root), the depth of a node n refers to the path length from n to Root, and is denoted as dp (n); n is a radical of_G(n) represents a set of nodes adjacent to node n in G; degree of a node in G is denoted dgr_G(x) And the degree of a node in T is represented as dgr_T(x) (ii) a The degree of one T in G is recorded as dgr_G(T) is the entry of the edge set E for G belonging to V_TThe total number of edges of the rendezvous node; similarly, the number of edges in T is dgr_T(T)＝|V_T|-1；

The NR encoding table of a tree T is an ordered list in which each node NR covers four elements (n, id, dp, dgr): respectively representing nodes (which can be identified by an autonomous domain number ASN in an inter-domain routing system), indexes, node depths and node values; the arrangement order between the nodes NR needs to satisfy: firstly, the nodes of each subtree are continuous, and secondly, the root of each subtree is arranged in front of the nodes; for a node n, according to the NR notation, id (n) indicates its index value, dp (n) and dgr_G(n) respectively representing the depth and the value of the depth; for a tree T, because of the sequential characteristic of depth-first search for nodes, when NR coding is implemented based on the depth-first rule, an unvisited node is searched, and the node and the corresponding depth value and the corresponding value can be added into an NR coding sequence;

encoding NR of a spanning tree F, namely representing Forest (FoR), and merging NR of each tree T in the F; since a forest contains multiple trees, a dual (p) can be used_T,dgr_T) A tree is represented, the former representing a pointer to the tree T and the latter representing the value of the tree.

3. The inter-domain route recovery method based on the degree-constrained minimum spanning tree of claim 1, wherein: in the fifth step, the FT key node selection algorithm KeyNodeSelectionForFT () is used for calculating a new tree T in FT_dstMiddle node T, and migrated subtree T_originR in (1); the fundamental migration fundamental transfer () algorithm is mainly used for constructing a new forest aiming at a typical scene that a certain key node in an inter-domain routing system fails after BGP-LDoS attack and effectively meeting the mathematical model requirement of a minimum spanning tree with degree constraint.

4. The inter-domain route recovery method based on the degree-constrained minimum spanning tree of claim 1, wherein: in the sixth step, the CT key node selection algorithm keynode selection nfortoct () is intended to calculate the migrated tree T_originR in (1); pruning a node f; new tree T_dstNode t in (1); the complex migration ComplexTransfer () algorithm is more complex relative to FT operation, and mainly aims at a situation that a plurality of adjacent autonomous domain nodes fail after an inter-domain routing system is attacked by BGP-Ldos, and utilizes a CT algorithm to generate a minimum spanning tree with a constrained degree so as to implement route recovery; the complex migration ComplexTransfer () algorithm effectively satisfies the mathematical model requirements of the minimum spanning tree of the degree constraint.

5. The inter-domain route recovery method based on the degree-constrained minimum spanning tree of claim 1, wherein: in the fifth step and the sixth step, in the process of node migration and change, the process is recorded in a mode of creating and gradually perfecting a coding matrix by using a node migration coding algorithm TransNodeS Encode ().